Beyond Information

A Major Paradigm Shift Is Coming

2009-01-28T21:16:00.001-08:00

A Major Paradigm Shift Is Coming

I am working on research that will result in a major paradigm shift that will turn out to be as significant to science and society as that of the shift from the Ptolemaic world view to that of the Copernican world view. My research has resulted in the discovery of two entirely new classes of representation that are both mathematically consistent and complete.

Why is this important? All of logic, mathematics, computation, and science are currently based on the theory of information. Godel's Incompleteness theorems proved that all formal systems above the complexity required to represent Peano arithmetic are incomplete, or inconsistent, or both.

The cause of incompleteness and inconsistency is not the concept of a formal system itself. The cause is the underlying representation of information formal systems are represented in terms of. Information is an indirect representation. It can only represent things INDIRECTLY. Information can not represent ANYTHING DIRECTLY. All indirect representations (of any complexity) are necessarily incomplete because they rely on something outside themselves, the mind of an intelligent observer, to decide the meaning of the bits and symbols represesented by information. The information does not represent meaning. The meaning of information is inferred by an external system, namely the observers brain. The internal operation of the observer's brain is not based on the representation of information, any more than the physical existence of the universe is. Just because our brain can interpret the meaning of information, it does not mean that our brain's operation itself is based on the representation of information. The belief that the brain's internal operation is based on the representation of information is a fallacy. I have proven this.

The problem for science is, the physical universe is complete and consistent, but our logical and mathematical representation of it IS NOT. Information is the wrong basis for the representation of physical existence. Information is incapable of representing the universe completely or consistently. For example, physical existence does not have any representation for the number zero. Physical existence can not and does not have a physical representation of nonexistence. Nonexistence does not exist as long as spacetime and dimensionality exist. Zero is a placeholder in the representation of information for the representation of nonexistence, or the representation of a possible existence. Nature does not represent the possible. It only represents that which actually exists. In terms of information, it is as if Nature only represents the ones.

Because nature only represents what actually exists phyically, nature does not have to make any decisions to represent existence or the physical configuration of the state space of existence. Nature does not have to interpret the meaning of information. The laws of physics create and enforce themselves because they are based on a complete consistent representation of existence that can ONLY represent that which exists. The laws of physics exist because they are the only possible laws that nature can represent using the direct representation of existence. There are no decisions to make. Only man wastes bits, energy and time representing the nonexistent. Nature is exponentially less complex. Since existence exists, and its representation cannot be based on information, its representation must be based on another form of representation. All indirect representations are incomplete and or inconsistent as Godel proved. The logical converse of an indirect representation is a direct representation. The converse of an incomplete, inconsistent, indirect representation is a complete, consistent direct representation. The representation of existence is based on a complete and consistent direct representation.

The universe is the transfinite recursion of the direct upper ontology of existence. Its recursive operator is based on the composition of symmetric differences between existence and incomplete (aka partial) nonexistence.

Using this representation one can generate new forms of logic and mathematics exponentially more powerful than those based on information. These mathematical forms provide a complete and consistent description of the universe. This description literally generates and enforces all the laws of physics. It can describe the creation of the universe and the evolution of everything in it starting from the bosonic singularity of complete nonexistence, where complete nonexistence is defined as the absence of all spacetime, matter and dimensionality. It describes what causes the quantization of energy. It describes what causes symmetry. It describes what space and time are and how they are formed. It describes the cause of the big bang and the lifecycle of the universe. It describes what happens inside the event horizon of a black hole. It describes the cause of the zero point field. It describes the cause of mass and the cause of gravity. It describes the cause of zitterbewegung. It describes the cause of subatomic structure and ultimately, the cause of all higher order forms of matter and energy in the universe. It provides the key to a complete understanding of physics.

My two main discoveries include:

1) The direct upper ontology of the representation of physical existence. I have discovered an upper ontology that is one-to-one isomorphic to the direct representation of physical existence. In other words, I have discovered a method that will allow us to create a direct one-to-one mathematical representation of the physical existence of the universe. Physical existence itself is a kind of representation, but it's representation is not based on information. Its representation is based on, and is, the transfinite recursion of the direct upper ontology of existence. By using that representation in a computer, it will allow us to directly model the creation of the universe, the creation of everything in it, and the relations between everything in it in context. Unlike conventional upper ontologies that are designed to be a foundation for lower level domain specific ontologies, the upper ontology of existence eliminates the need to create any domain specific ontologies. This should reduce the complexity of the mathematical representation of complex systems combinatorially. It will also allow us to conveniently represent the existence of phenomena whose behaviors vary depending on the context they exist in.

Black Holes

Given upcoming events at the LHC we better make sure we really understand black holes before we create them. The current theory of black hole formation and operation is based on information theory. It is incomplete.

Current theories as to what goes on inside the event horizon of a black hole are incorrect. Black holes are not created, nor do they operate as current Physics predicts. Specifically, their power source and the source of their gravity field is not the energy in the particle stream that creates them. A black holes power source is derived primarily from the collapse of the fermionic field that composes spacetime inside the event horizon. Exceeding the speed of light destroys the consistency of the representation of existence and causes the collapse of the fermionic field that composes the zero point field that composes the dimensions of spacetime. When it collapses, the fermionic field transforms to its inner representation, a bosonic field. Bosons do not occupy spacetime. That is why bosons can all occupy the same non-dimensional "point". That is why black holes cause singularities. The vast majority of the energy contained in a black hole comes from the conversion of the fermionic field to a bosonic field.

Inside the event horizon the zero point field that composes the structure of spacetime has collapsed. Dimensionality ceases to exist. Energy cannot escape the black hole because it has no spacetime to travel thru, not because it can't travel faster than the speed of light.

The main power source for a black hole is the difference between the zero point field energy outside the event horizon and the localized nonexistence inside the event horizon. A black hole is the only phenomena in the universe that frees up all the energy in the zeropoint field and makes it available to do work. The almost limitless zero point field energy outside the event horizon flows to "ground". It causes the black hole to ingest spacetime and collapse its fermionic field, converting it to a bosonic field and allowing it to collapse into a singularity.

The conservation of energy can not be used to calculate the energy in a black hole becuase it does not consider the difference in the zero point field energy that composes spacetime outside the event horizon and the absolute zero energy density inside the event horizon. Evaporation of the black hole (if it evaporates) exposes the singularity at its core, and allows the naked singularity to convert most of its energy back into its outer representation - a fermionic field and the subsequent creation of the zero point field and space time. The explosive expansion in space time that results transports massive amounts of high energy gamma rays as it expands and the zero point field reforms itself. This is the cause of gamma ray bursts. In the extreme case of the primordial black hole, it causes the big bang.

This paper also identifies a new mechanism for the creation of black holes that makes it unlikely they would be created by cosmic rays, but increases the likelihood they may be created in a particle accelerator. Be advised, the energy in the particle stream used to create a black hole is only the energy needed to trigger the formation of the black hole. It does not account for the energy the black hole will ingest and convert from the spacetime surrounding the event horizon. Creation of an artificial black hole could be catastrophic. Due to variability in the way a black hole could be created in a particle accelerator, it is not possible to quantitatively ascertain the amount of energy that would be released if it evaporates and exposes its singularity. In addition, the mechanism thought to account for black hole evaporation was based on the representation of information. It is not reliable.

2) The universal representation of thought. This appears to be the basis for the biological neural knowledge representation and upper ontology responsible for all human thought, perception, awareness and consciousness. It solves the unitary binding problem in neural science. It provides a completely new model of computation and a completely new coding theory that will allow us to develop sentient computer systems that can perceive, think and understand the meaning of information and knowledge from their own first person direct perspective in context. Just as the universe is the transfinite recursion of the direct upper ontology of existence, the mind results from the transfinite recursion of the direct (and indirect) upper ontology of abstraction. Both the representation of thought and the representation of existence form the basis for mathematical systems exponentially more powerful, and more compact than the representation of information. In fact the representation of thought provides exponential compression relative to the direct representation of existence. That is why we can store so much knowledge within the limited volume of our craniums.

Philosophical Basis

Some time ago, I discovered an inconsistency in the Philosophy of information, in the principles of ontological neutrality that has been lurking there since the early 1960's. Its significance was apparently overlooked.

ON.2 (It from Bit) is inconsistent with ON.1, ON.3, and ON.4. See http://plato.stanford.edu/entries/information-semantic/#1.6 for the definitions of these philosophical principles. Proof of the inconsistencies in ON.2 relative to the interpretation of physical existence can be found in earlier entries in this blog.

I was able to resolve the inconsistencies by separating the ontological representation of existence from the ontological representation of information. This preserves ON.2 but restricts its domain to that of communication and computation.

By creating a separate ontology for existence, it allows each thing in existence to represent itself from its own first person direct perspective in context. It also accounts for the ubiquitous fact that each thing that exists is composed of other things. Its existence is defined in terms of how it relates to the things it is composed of and how it relates to the things in its external environment. The complexity of the representation and ontology of existence is constant, and independent of the number of types of things in existence. By contrast, the complexity of the representation of information grows combinatorially in the number of types of things it represents.

The ontology and direct representation of existence eliminates the problem of the observer in Physics and in physical existence, and it provides a mechanism that automatically accounts for the consistency and completeness of the totality of existence itself. It also provides a physical existential ontology that can solve the horizon and flatness problems in cosmology without violating the speed of light as inflation does.

Information is Incomplete and too Complex to Represent the Totality of Existence

Imagine you are a proton. A proton can't represent itself from the 3rd person indirect perspective of an observer. Which observers' perspective would it choose to represent itself from? Which observers' frame of reference would it represent itself from? If you are a proton, you must experience forces from the perspective of your own existence, relative to the spacetime context and frame of reference you exist in. You can't experience forces as seen from the third person perspective or reference frame of any observer.

While we can model protons or most other things indirectly using information and current mathematics, it quickly becomes very complex to model large systems of interacting fields and particles mathematically, especially if their behavior varies based on the context they exist in. For example this makes it extremely difficult or impossible to solve many body problems in quantum mechanics for systems larger than a hydrogen atom without simplifying them into collections of simpler problems, or ignoring parts of the problem to create a problem simple enough to solve. Using the ontology and direct representation of existence, it should be possible to model and solve very large many body problems directly because the ontology and direct representation of existence model context dependent relations directly. Using the ontology and direct representation of existence, the encoding and representation of many body problems is dynamic and the representation alters itself dynamically based on the changing contextual relationships between the bodies in the problem. The result should be a combinatoric reduction in the complexity of the equations required to solve many body problems, and a combinatoric increase in the size of many body problems we can solve. Consequently, further development of this theory could lead to rapid advances in our knowledge of quantum physics and relativistic quantum field theory among other things.

Seen from this perspective, the idea of representing the physical existence of the universe in terms of information is ludicrous. Protons aren't physically composed of bits or information. In addition representing the physical existence of protons using information would violate cause and effect because physical existence itself is a representation. Physical existence is logically and physically prior to observation. The universe existed long before conditions in it could support life. Nobody could have been around to represent existence from the third person indirect perspective of an observer. Therefore, the physical representation of existence cannot be based on information. It cannot be based on any representation that requires an observer, other than each particle itself, because if we go back in time to the existence of the first photon in existence, only the first person perspective of the existence of the first photon could have been available.

Each thing that exists has to represent itself from its own first person direct perspective. This is true whether we are talking about subatomic particles, energy quanta, atoms, molecules, proteins, neurons, people, rocks, trees, stars, galaxies or anything else that exists. The only representation that is the same across all of existence is the first person direct representation of each thing that exists. The representation of physical existence emerges from the composition of the first person direct representation of each thing that exists and the relationships among those things. All of those relationships and all of those representations are based on and constrained by the upper ontology of existence.

The representation of information was designed to support human communication. It wasn't designed to represent the physical existence of fields of force and subatomic particles. This has been known since the 1960's in Philosophy, but it looks like nobody noticed what the implications of those inconsistencies implied. Specifically:

1) By separating the ontology of information and the ontology of existence, we can create a direct one-to-one representation of the existence of the physical universe. We can generate a direct set theoretic representation of physical existence from the transfinite recursion of complete nonexistence and a nilpotent symmetric difference in nonexistence in a manner analogous to the way the Von Neumann Universe of mathematics is generated from the transfinite recursion of an empty set and the set that contains the empty set. This will provide the basis for a new kind of direct set theory and direct mathematics that is isomorphic to physical existence itself. It will also provide the ontological foundation required to further the development of quantum computation.

2) Human communication and computation are based on the transfer or communication of information between computers and individuals, but the requirements necessary to support communication are not the same as those needed for the computation of meaning from the first person direct perspective in context. Why should the human brain be based on the requirements of information? Most parts of the brain evolved long before the development of speech in our species. Why should we base computation on the requirements of a mathematical theory of communication? Why not base it on the requirements of abstract computation, and then translate the results to and from information for external communication? That is what the brain does. It turns out evolution was a lot smarter than we were. Evolution figured out a way to avoid the limitations of Goedel's Incompleteness Theorems, and a way to compute everything using a single universal computational algorithm, and a single knowledge representation with absolutely no domain limitations. What's more it does so with constant computational complexity, while computational power scales combinatorially for each stage of neural processing, and storage is compressed as a combinatorial of combinatorals for each subsequent stage of neural processing.

I developed a separate ontology for the direct representation of existence that looks like it will be able to explain all of Physics, even the cause of the Big Bang itself. I.e., where did all that energy come from? It also explains the first cause of symmetry, it explains what energy is, not just what it can do. It explains why existence is quantized, it explains what created spacetime and what it is, it provides an alternative explanation for black holes, it provides a much more intuitive explanation for quantum mechanics, and it looks like it may explain the cause of mass. It also predicts the Higgs mechanism is incorrect. It disproves the many worlds interpretation of quantum mechanics. With some further development, we should be able to use it to solve very large many body problems.

It looks like my thesis on the direct representation of existence is consistent with most of the standard model except:

1) It includes the physical existence of spacetime in the form of a fermionic field with spin 1/2 that assembles the zero point field and creates the four dimensions of spacetime.

2) It provides an alternative explanation for the expansion of the universe.

3) It provides an alternative explanation for the cause of black holes and the source of their gravity and power.

4) It provides an additional law of nature more fundamental than the conservation of energy - that causes the conservation of energy.

5) It provides an alternative explanation for the cause of mass.

6) It predicts the Higgs mechanism is incorrect and that the Higgs' Boson does not exist.

7) It identifies the root cause of the quantization of energy.

8) Instead of representing existence using a fixed number of dimensions, it represents it in the minimal combination of dimensions required to represent each thing in existence with maximal entropy. The mathematical system this forms allows one to solve systems of equations independent of the dimensionality of that which the system represents. It also represents everything in context so the representation automatically accounts for all contextual dependencies.

9) It eliminates the need for observer relative or observer dependent reprsentation.

10) It ensures the consistency and completeness of the universe.

11) It eliminates the need for a "decider" to determine which possibilities exist and which are only potential.

----------------------------------------------------------------------------------------------

The Universal Representation and Ontology of Thought

I have also discovered what appears to be the ontology and neural knowledge representation responsible for the representation and computation of all abstract human thought, perception, and consciousness. It provides a new model of computation and a new coding theory that will allow computers to represent the meaning of information from the first person direct perspective in context, and understand its meaning. It will also allow computers to perceive the world around them and form their own subjective experiences. The representation of thought will allow the development of sentient computers that compute directly in terms of abstractions and concepts from the first person direct perspective in context.

Like the ontology of existence, the ontology of thought is an upper ontology that eliminates the need to create any domain specific ontologies. It is based on the ontology of abstraction itself. The ontology of thought is one-to-one isomorphic to the spatial topology of biological neurons. Everything we can think, experience, feel, perceive, or do can be represented as an abstraction. Neurons in the brain represent everything we think, experience, feel, perceive, and do as abstractions. Each neuron is a living expemplar of a whole collection of related abstractions.

This is a major advance in computation. Not only will we be able to create sentient computers that can think and understand meaning using the same knowledge representation used by our brains; it provides a model of computation that has constant complexity, independent of the complexity of the problem being solved. Processing capacity scales geometrically. If we assume each neuron in the network can compute the result of a 100 term abstract equation, then:

- First level neurons can each compute a 100 term equation.
- Second level neurons can each compute a 10,000 term equation.
- Third level neurons can each compute a 1,000,000 term equation.
- Fourth level neurons can each compute a 100,000,000 term equation.
- Fifth level neurons can each compute a 10,000,000,000 term equation.
Etc.

In addition, computation time is constant at each level. If each level takes 5 mS to compute its result, we could compute the results of n 1.0 x 10^10 term abstract equations in 25 ms where n is the number of neurons in each layer of the network.

Doing this in realtime would require development of a new type of massively parallel hybrid neuromorphic CPU, but even with conventional hardware, a lot can be done, even with current computers. The computational model is very, very efficient. It uses a universal of computation. It is based on a single function that can compute anything a sentient system can percieve, feel, think, learn, understand, or do from the first person direct perspective of the system itself.

Storage is also extremely compact. Storage is compressed combinatorially at each layer in the network. Compression efficiencies scale in direct proportion to computational capacity so compression is geometric combinatorial in the number of levels in the network. Hence the amount of knowledge the network can store is astronomical.

Even better, the direct representation of existence and the universal representation of thought are both complete and consistent and have no domain limitations. I'm not just talking truth functionally complete and consistent. I am talking universally complete and consistent. As in the ability to compute anything in the universe with no domain limitations.

These representations both get around the limitations of Goedels Incompleteness Theorems. This will allow us to develop new set theories and new forms of mathematics that are universally consistent and complete. We'll be able to work through logical problems and compute anything in the universe, or anything we are capable of thinking using a single ontology and a single knowledge representation with absolutely no domain limitations.

That's pretty powerful stuff.

Big changes are coming.

Stay tuned for further developments.

Ontology

2009-01-23T19:42:00.000-08:00

Ontology

Since the direct representation of existence and the universal representation of thought are both based on ontologies, a brief review of ontology is in order.

According to Tom Gruber, an ontology is an explicit specification of a conceptualization (Gruber, 1993). That is, an ontology is a description (like a formal specification of a program) of the concepts and concept relationships that are of interest in a domain of discourse. The term “ontology” is borrowed from philosophy, where an ontology is a systematic account of existence.
For knowledge-based systems, what “exists” is exactly that which can be represented.

Formally, an ontology is the statement of a logical theory; i.e, an ontology is the (representation / description / encoding) of a logical theory. Most ontologies defined to date have been based on indirect representations. Thought is represented in terms of and relative to each agents’ universal ontolology.

When we represent the knowledge of a domain in a declarative formalism, we call the set of objects that can be represented the universe of discourse. This set of objects, and the describable relationships among them, are reflected in the representational vocabulary with which a knowledge-based program represents knowledge. Thus, we can describe the ontology of a program by defining a set of representational terms. In such an ontology, definitions associate the names of entities in the universe of discourse (e.g., classes, relations, functions, or other objects) with human-readable text describing what the names are meant to denote, and formal axioms that constrain the interpretation and well-formed use of these terms.

We use common (shared) ontologies to describe ontological commitments for a set of agents so that they can communicate about a domain of discourse without necessarily operating on a globally shared theory. We say that an agent commits to an ontology if its observable actions are consistent with the definitions in the ontology. Pragmatically, a common ontology defines the vocabulary with which queries and assertions are exchanged among agents. Ontological commitments are agreements to use the shared vocabulary in a coherent and consistent manner. The agents sharing a vocabulary need not share a knowledge base; each knows things the other does not, and an agent that commits to an ontology is not required to answer all queries that can be formulated in the shared vocabulary.

In short, a commitment to a common ontology is a guarantee of consistency, but not completeness, with respect to queries and assertions using the vocabulary defined in the ontology.

A domain ontology (or domain-specific ontology) models a specific domain, or part of the world. It represents the particular meanings of terms as they apply to that domain. For example, the word ‘card’ has many different meanings. An ontology about the domain of poker would model the ‘playing card’ meaning of the word, while an ontology about the domain of computer hardware would model the ‘punch card’ and ‘video card’ meanings.

In information science, an upper ontology (top-level ontology, or foundation ontology) is an attempt to create an ontology which describes very general concepts that are the same across all domains. The aim is to have a large number of ontologies accessible under this upper ontology. It is usually a taxonomy of entities, relationships, and axioms that attempts to describe the representation of those general entities that do not belong to a specific problem domain.

Representational Encodings

2009-01-23T17:17:00.000-08:00

Representational Encodings

The type of encoding used by a representation confers upon it unique properties and abilities enabling each type of representation to serve its distinct purpose. Without their distinct encodings, the three types of representation would not possess the properties and abilities required to represent existence, thought and information respectively. Only by understanding the advantages and disadvantages of the different types of encodings can we know how best to utilize each encoding and each representation that uses it.
There are two basic types of representational encodings: Fixed, and Relative.

Fixed Encodings
Fixed encodings represent each symbol with a constant fixed code or fixed numeric value, or fixed pattern. Information uses fixed encodings. For example in a computer, the ASCII code for the letter ‘A’ is always decimal 65 or binary 01000001. Every computer that uses the ASCII encoding represents an upper case A as the decimal number 65. In printed text using the Latin alphabet, the uppercase letter ‘A’ is always represented by a character that looks like ‘A’. Fixed encodings are typically based on standards, conventions or agreements. Fixed encodings are context free. The value of the code used to represent each symbol is fixed. It does not change as a function of the context it is used in. Information uses fixed encodings. Fixed encodings are well suited for communication. Their weakness is they are not very compact, and they do not scale well when representing complex, context dependent information.

Relative Encodings
In contrast to fixed encodings, relative encodings have no public fixed “symbols”, fixed codes, or fixed values. Relative encodings are private and context dependent. Relative encodings encode the representation of particulars in terms of how they ‘relate’ to ‘other particulars’, where the ‘relations’ and ‘other particulars’ are defined relative to the context in which they are used, or they are represented by an instance of a previously defined relative encoding within the context of definition of that which they participate in the definition of.

Both fixed and relative encodings can represent how things relate to each other, but they do so differently. Fixed encodings represent relationships external to the encoding of an entity; that is the relationships are used to define the intension of an entity, but the encoding of the relationships themselves is independent of the context they are used in. For example, in a fixed encoding the representation and meaning of an addition operator is defined outside of the context in which it is used. Its’ encoding and meaning are not affected by the context it is used in. In a fixed encoding, the relationships are represented by the encoding, but they are defined external to it. Hence, in a fixed encoding, the relationships have an existence and a coding independent of their use in the intensional representation of an entity.

Relative encodings embed the encoding and representation of the relationships between entities as part of the representation of the entity itself. The entity being defined encodes the representation of the relationship relative to, and in terms of the entities own existence or direct representation. The relationships are internal to the encoding of the representation and are defined by, in terms of, and relative to it. The encoding of the relationships is inseparable from the encoding of that which they relate. In a relative encoding, the relationships do not have independent context free definitions. They are only defined by and only have meaning relative to the context they are used in. This is a critical distinction. With a relative encoding, either all the parts of the representation of a particular are embedded inside the particular, or the particular does not exist.

Relative encodings encapsulate the representation of their component parts. Fixed encodings do not. With a fixed encoding, each part of the representation is separable and context independent. Fixed encodings allow partial representations of particulars. Relative encodings do not. The use of relative encoding to encode the direct representation of existence is the cause of the bivalence of existence. At the level of quanta in Physics, quanta exist fully or not at all. Empty space has physical existence because it has dimension. Distances can be measured in space. If space did not exist, there would be no measurable distance between objects in space. Space can be curved. Space also contains vacuum energy fields, also known as the zero point field, or dark energy, thought to be responsible for the cosmological constant and the accelerating expansion of space. Additional physical evidence for considering the physical existence of space will be covered in more detail later. Fundamental particles (i.e., fermions) and bosons also exist fully or not at all. Nothing physical partially exists at the fundamental level of physical quanta.

The relative encoding of existence is also the cause of the Pauli Exclusion Principle in Physics. It is the reason matter cannot pass through matter, even though according to the standard model of particle physics, matter is known to be 99.999999999999% empty space. Matter is composed of curved or knotted zero point energy vacuum fields. The space-time encapsulated in matter is part of the representation of matter. It is not possible to separate matter from the space-time that composes it because the direct relative encoding of matter encapsulates the representation of the space-time from which the matter is composed. Removing the space-time from the representation of matter, or changing the space used in the representation of matter would be the same as removing part of the representation of matter. It would break the encapsulation of the representation of existence, which would make it inconsistent and the matter would cease to exist. It is not possible to break the encapsulation of the representation of existence without destroying it. The encapsulation of the representation of existence is a fundamental property of existence.

The encapsulation of the representation of existence is responsible for the bivalence of existence. If the existential representation were not encapsulated, existence would not be bivalent; i.e. quanta could partially exist, and quantum states would not exist, and the universe would not exhibit quantum behavior or operate according to the laws of Quantum Mechanics . The encapsulation of the representation of existence is the cause of all quantum states in Physics. If the fundamental building blocks of existence did not have quantum states, then the conservation of nonexistence would be violated (we'll cover this later after we formally define the representation of existence), it would be possible to destroy nothing, and the laws of Physics would be inconsistent.

Without quantum phenomena, the fundamental building blocks of existence could partially exist and existence would be continuous, incomplete and inconsistent instead of quantized, complete and consistent. Partial existence does not occur at the quantum level. Nothing that exists can exist half inside and half outside the universe. An individual quantum property must be in one quantum state or another. It cannot exist at a level partly between two different quantum states. Quantum behavior is a fundamental property of existence precisely because it is dependent on the representation of existence. It is a necessary fundamental property of existence because of the bivalence between existence and non-existence and the encapsulation of the representation of existence.

Representation

2009-01-21T18:43:00.000-08:00

Representation

The Merriam Webster’s Collegiate dictionary definition of representation is something that serves as a specimen, example, or instance of something[1].

Before we dive into the detailed representation of thought, existence, and information, we need to take a step back and examine the fundamental nature of representation in general. Although representation is one of the most fundamental phenomena in existence, the most fundamental question: what is it? – has rarely been answered directly.

The overwhelming majority of work on representation has been based on the symbolic representation of information. This includes the development of logic, mathematics, and information systems.

Information and everything based on it only address one of the three fundamental types of representation. It is important to view the entire landscape of representation so we can see how logic, mathematics, and information relate to the other fundamental types of representation. It is also important to see if some other fundamental type of representation is better suited to the representation of thought than a representation based on symbolic logic, mathematics, or information. We need to look beyond the symbolic representation of information. If we confine ourselves to only one of the three fundamental types of representation, we limit our ability to reason to that which can be represented by that single fundamental type. We should not limit our ability to reason needlessly. We certainly should not do so blindly.

An Orthogonal Classification of Representation
In the most general sense, representations can be classified along two orthogonal principal axes: The first axis of representation is the direct - indirect axis. The second is the intensional - extensional axis. These axes form an abstract two dimensional concept space within which we will map and analyze the different fundamental types of representation.

The Direct - Indirect Axis of Representation
There are three fundamental classes of representation along the direct – indirect axis; direct representations, indirect representations, and universal representations.

[1] Merriam Websters Collegiate Dictionary, 11th Edition, Meriam-Webster, Inc., 2003

Direct Representation

2009-01-21T18:27:00.000-08:00

Direct Representation

A direct representation is the thing itself; i.e., everything that exists in the universe is a direct representation of itself. For example, the direct representation of a particular proton is that particular proton. In fact, there is, and can only be, one direct representation of each particular thing that exists in the universe. Hence, the referent (i.e., extension) of a direct representation IS directly composed of the representations intension, where the extensional representation is the only instance of the thing represented. Composition in the sense used here is equivalent to containment; i.e., in a direct representation, the extension is composed of its intension because it contains its intension. The existence of the intension is equivalent to the existence of the extension. Everything that exists represents itself. In short, existence represents itself. This can be represented symbolically by the equation: Existence = Representation. Mathematically, a direct representation is endomorphic. Each particular or “thing” that exists in the universe is the only direct representation of its own existence. Direct representations are “first-person” representations. They represent things from the first person “inside-out” perspective of the things themselves instead of from the third person indirect “outside-in” perspective of an external “observer”. In a direct representation, any calculations, computations, or processes occur directly on, and in terms of the actual thing itself, and hence directly on its own representation. The importance of direct representation has been seriously underestimated. Development and application of direct representations is the key to solving many of the deepest unsolved problems in Philosophy, Physics, Cognitive Science, Artificial Intelligence (AI), and the theory of representation. One of the most difficult unsolved problems in logic, AI, and cognitive science is how to create a knowledge representation that can perform computation from a “first-person” perspective. How do we make a computer self-aware? How do we give a computer the ability to represent and understand meaning from a first person perspective? How do we give it an intrinsic sense of self; e.g., cogito ergo sum? I think, therefore I exist. How do we create a conscious machine? Direct representation is the key to the solution to ALL of these problems.

Direct representation is also the key to the creation, representation and ongoing construction and operation of existence itself. Everything that exists must have some representation. Without representation, there can be no existence. The direct representation of existence IS existence. Furthermore, things must be able to exist independent of the existence of an observer. Existence cannot represent itself from the perspective of an observer. Existence is logically prior to observation. Thus, the representation of each thing that exists must exist independent of the existence of an observer. Just because nobody is around to observe a thing does not mean that thing does not exist. Space-time, matter and energy were all present in the universe long before there were any observers to experience them. This means the representation of existence cannot depend on an observer in any way whatsoever. The representation of existence must be entirely observer independent. The only way to eliminate the observer in representation is to define a type of representation in which everything that is represented is its own observer. We must use an endomorphic representation in which the referent of the representation of a thing refers to the things own representation. Everything in existence is then represented from its own “first person” perspective. In existence, things are not represented relative to an observer. The representation of everything in existence is represented relative to itself. Existence represents itself. Understanding this is critical. If you do not understand this, you will never fully understand existence. Do not despair if you don’t fully understand this immediately. Direct representation is actually very simple, yet it can be a difficult concept to grasp because we are so used to representing things indirectly to express them as information.

Direct representations are also context dependent. Direct representations always represent things in context. Their representation is defined in terms of and relative to the context in which the representation exists. Everything that exists exists in, and is represented relative to some context. By contrast, indirect representations are context free. In an indirect representation, the representation does not vary as a function of the context the object is contained in or used in. For example, the representation of the letter ‘e’ does not vary as a function of the word it is contained in or as a function of the sentences it is contained in. The same word can represent different meanings in different contexts, but it is spelled the same way in every context. In an indirect representation, the meaning is not encoded as part of the representation so the fact that the meaning of a word may be interpreted differently in different contexts is independent of the representation of the word.

Direct representations are encapsulated because they are defined and encoded relative to, and in terms of, the context they are represented in, and because each thing represents itself. Consequently, each particular requires its own representation. The representation of each particular can only be used once in the context it is part of. There is always a one to one relationship between the representation and its only instance. By contrast, indirect representations are unencapsulated. In an indirect representation, the representation of a particular is indirect. The extension is a substitute for the thing represented by its intension, not its intension itself. In addition, in an indirect representation, the encoding of the relations that define the intension are independent of the encoding of the intension, not defined relative to, and in terms of it. Hence, in an indirect representation, the ontology does not constrain the completeness of the intensional representation, so it can be incomplete unless constrained by domain specific ontological consistency rules outside the ontology itself. In an indirect representation there can be a one to many relationship between its representation and its instances. Many instances of the same thing can occur in many different contexts. In a direct representation the extension is an identity for its intension.

Direct representation can seem very odd because it is counter to the way we normally represent information. We must use information to communicate. The meaning of information is always defined and understood relative to an observer. A book does not understand the words it contains. The letters and words in a book have no meaning, in and of themselves. The meaning is only in the mind of the book’s reader. Each observer interprets and understands the meaning of information relative to their individual state of knowledge when they read the book. The point is, the meaning of ALL information is inherently relative to an observer. Yet we know logically that the representation of existence cannot depend on ANY observer. Therefore, the representation of existence must not be based on information. If the representation of existence is not based on the representation of information, but we only use information to communicate and reason about existence, we constrain our ability to reason to that which can be represented and communicated using information. If existence itself is not represented using information, then how can we hope to fully understand it? If we base our understanding solely on information, our understanding will always be constrained by the limits of the representation of the information, logic and mathematics we use to reason and communicate it.

To understand existence fully, we must create and use a system of representation that has the same, or fewer limits and constraints than the representation of existence itself. We must create a logic and mathematics based on the first person direct representation of existence instead of the third person indirect representation of information. After we do this, things that are extremely complex and difficult to understand, represent and compute using information will be simple and optimally efficient. Once we use the proper representation, we will be able to represent how anything relates to anything else in any combination of any number of dimensions in any context and perform logical and mathematical operations irrespective of the dimensionality of the representation. Put in less abstract terms, we will be able to perform arithmetic directly on systems of any combination of dimensions. We will be able to represent everything in its most efficient number of dimensions and perform all calculations the same way regardless of the dimensionality of the representation or the complexity of the computation. For a less abstract example, imagine being able to directly add vectors of any combination of different dimensions together, or imagine being able to directly take the dot product of vectors of any combination of different dimensions. Imagine a single operation that is the universal of computation in the same sense that an entity is the universal of information. In terms of the representation of thought, imagine being able to calculate directly in terms of concepts and abstractions at the speed current computers calculate in bits. That is the magnitude and import of what I am talking about here. The potential gains in human understanding through application of this knowledge boggle the mind.

Our ability to understand the representation and operation of existence is not as hopeless as it may seem from the discussion above. We are all born with an internal knowledge representation that can transcend and surpass the constraints and limitations of logic and information. The human brain’s knowledge representation is actually less constrained, and more capable than the representation of existence. It is not our innate ability to reason that is fundamentally limited. It is our inability to fully communicate the results of our reasoning via the translation to and from information that limits our understanding.

We think directly at the level of concepts and abstractions. We just cannot communicate and transfer that knowledge directly to others. Instead, we have to convert it to information first. It is not that we cannot represent anything we want to with information. Subject to language limitations, we can. It is just impractically complex, lengthy, and time consuming to do so.

Information does not encode the meaning of knowledge. It can only encode information about knowledge. Normally, pragmatic time, space, and complexity constraints only permit us to encode a minuscule fraction of a small portion of selected aspects of our knowledge for communication. Even then, the information transmitted is subject to misinterpretation and may be misunderstood by its recipients if their preexisting knowledge of the topic of communication is not sufficiently similar to that of the sender. Even worse, if we only think in terms of symbolic information, we hobble our intellect. We limit our thinking to that which can be represented by information, and we slow our thought by making things combinatorially more complex than they really are if we allowed ourselves to think and reason directly in our brain’s direct internal representation.

Have you ever wondered why you can think much faster than you can reason using symbolic logic, or perform mathematical calculations? Have you ever wondered why a picture is worth a thousand words? Have you ever wondered why we can grasp complex relationships almost instantly with the help of a good illustration or recognize an image in a picture almost immediately, yet trying to understand the same content if it is described in words or mathematical equations is slow and error prone if it can be expressed in words or equations at all? The same is true of listening to music, tasting a good wine, or smelling a flower. Representing these things using symbolic information is complex, slow, and often difficult or impossible. Sometimes we can teach ourselves specialized languages or specialized notations and train ourselves to do it but it really slows things down.

What if there was a way to think about, analyze and understand highly abstract concepts as easily as you can understand a picture? By understanding and internalizing the representation of thought, and the representation of existence, you will be able to do so. It will not happen overnight. At first, the change will be very slow, almost imperceptible. It will not seem like anything is different. Then you will catch yourself understanding how you thought about something right after you thought about it. Gradually, you will notice an increased ability to understand abstract topics like mathematics and quantum physics. The rate at which you can understand abstract topics will continue to accelerate. Learning the representation of existence and the representation of thought is the gift that keeps on giving. The only thing that will slow you down is the necessity to convert your understanding into words to communicate it and teach it to others. Alas, that cannot be avoided. Communication is only possible using the representation of information.

A block diagram that shows how things are represented using direct representation is shown below. In this diagram Thing1 is related to Thing2 by relation R1. It is also related to Thing3 and Thing4 by relation R2. The intension of the representation of each thing is composed of the representations of the things that compose it. Therefore the representation is fully encapsulated. All items are represented "by value", and each item is a singleton. In other words, each item has a unique identity and there is only one instance of each item. The consistency and completeness relations are part of the ontology of direct representation. No intelligent observer is required to define them, and no extra representation is required to represent them. In the representation of existence, representation = existence. We can use a variant of a direct representation in a computer to represent things directly, as long as we maintain a one-to-one relationship between each thing in existence and its representation in the computer. In other words, a direct representation is characterized by a one-to-one relation between the existence of each thing and its representation.

Indirect Representation

2009-01-21T18:24:00.000-08:00

Indirect Representation

Indirect representations are surrogates for something else. Indirect representations are “third-person” representations. They represent things from the third person “outside-in” perspective of an external observer. The referent of an indirect representation is whatever the representation represents. Indirect representations take many forms. Among the most developed are first order predicate logic and mathematics. Other types of indirect representations include computer programs, and various types of knowledge representations. A knowledge representation (KR) is most fundamentally a surrogate, a substitute for the thing itself, used to enable an entity to determine consequences by thinking rather than acting, i.e., by reasoning about the world rather than taking action in it [Davis et al, 1993]. As far as we know, no other species creates indirect representations at the high level of abstraction of homo sapiens. As far as we know, no other species creates persistent indirect representations, i.e., writing, or some equivalent. However, other species do communicate and the act of communication entails the use of indirect representations, so other species are capable of creating transient indirect representations. Human beings often encode indirect representations symbolically as information. However, indirect representation does not have to be symbolic. Indirect representations can be encoded in a wide variety of forms for communication.

A block diagram that shows how indirect representation represents things is shown below. This diagram represents the same relationships that were shown in the diagram of direct representation. Thing1 is related to Thing2 by relation R1. Thing1 is also related to Thing3 and Thing4 by relation R2. However, in indirect representation, all the representation is indirect. Thing1, Thing2, Thing3, Thing4, R1 and R2 are all represented indirectly. The actual representation of the thing that Thing1 refers to is located outside the representation of Thing1 itself. Thing1 and its representation are two different things. The same is true of every other thing and every relation that is represented. The advantage of this type of representation is that the definitions of things only have to be stored once, and then multiple instances of those things can refer to the same definition. This saves storage. However, the disadvantage is the representation is unencapsulated, and extra representation needs to be added if we want to make sure the representation is complete and consistent. In order to define the consistency and completeness conditions, an external intelligence must know what is to be represented and it must decide how to represent it. Contrast this with direct representation. For a direct representation, no intelligent observer is required to define consistency or completeness constraints nor do the constraints need to be represented explicitly. Instead they are represented implicitly by the ontology of the representation.

Universal Representation

2009-01-21T18:17:00.000-08:00

Universal Representation

It turns out there is also a third fundamental class of representations that has heretofore been overlooked. I call this a universal representation. Universal representations combine direct and indirect representation. They can represent themselves and everything else directly and indirectly. Universal representation is based on the representation of abstraction. Anything can be represented by an abstraction indirectly, including the representation of other abstractions, but abstractions themselves are represented and processed directly. This provides complete and consistent direct representation of everything indirectly while avoiding the inconsistency and incompleteness of pure indirect representations and avoiding the limited representational power of direct representations.

The key idea is to represent one and only one thing directly, but that one thing then represents everything else indirectly. The one thing that represents everything indirectly is the ontology of abstraction. We use a direct representation of an instance of the ontology of abstraction to represent each thing we want to represent indirectly. That allows us to represent anything directly as an abstraction, yet the abstraction represents things indirectly. This provides a direct representation of indirect representation. It directly represents everything indirectly. With indirect representations like logic, set theory and mathematics, we represent everything represented by direct representation indirectly. Logic, set theory and mathematics do just the opposite of what the brain does. Instead of directly representing everything indirectly, logic, set theory and mathematics try to indirectly represent everything directly. It is impossible to indirectly represent everything directly because the indirect representation of everything is too complex and it is inconsistent or incomplete or both. Doing things the other way around, the representation only has to represent one thing completely and consistently. If there is only one thing to represent in a domain of discourse, the only way for it to be incomplete or inconsistent is for it to be incomplete or inconsistent relative to itself. If a representation only has to represent one thing, the representation is simple enough that we can make it complete and consistent. This then allows us to avoid the adverse consequences of Gödel’s incompleteness theorems.

Fortunately, it is possible to represent one thing completely and consistently using information, provided the complexity of that one thing is not too great. Therefore, we can use a computer to indirectly represent the direct representation of one thing, and then use that one simulated direct thing to ‘directly’ represent everything else indirectly. We use the same strategy used by nature in the brain, but it is a little less efficient due to the additional level of indirection. Nevertheless, it still provides the means to represent everything indirectly completely and consistently.

The representation of thought is a universal representation. While we have not defined the terms and laid the prerequisite groundwork needed to understand the representation of thought, a brief introduction is possible.

In a universal representation, the intension and extension are direct, but the direct use of the extension within the representation of the intension is indirect. Consequently the intension defines meaning in context from the direct first person perspective, but the extension can be used in multiple contexts and be included as part of the representation of multiple intensions. In this case, the representation of the intension and extension are represented directly by value, but the use of the extension is represented indirectly by reference.

A neuron is a universal representation because its dendritic trees directly represent the intension of a concept and the intension of the set of abstractions that constitute the intensional representation of the concept. Detection of the direct satisfaction of the intensional conditions via the process of dendritic integration triggers the firing of the neuron’s axon which signals the existence of the concept extension and the existence of the particular abstraction extension it represents in all intensional contexts it participates in the definition of. All neural processing is direct, but the representation is simultaneously direct and indirect. The direct processing and direct representation entail self-awareness and first-person understanding of the meaning of concepts and abstractions from the first person direct perspective in context, while the indirect representation of the use of the extension entails third-person reasoning about external things at multiple levels of abstraction in terms of how those things relate to other things in context. If you do not understand this right now, do not worry. We will cover all of this later in much more detail after we present the prerequisite definitions and concepts required to do so.

The diagram below shows how the same system that was represented for direct and indirect representation is represented using a universal representation. From this illustration, you can immediately see how the ontology of a universal representation resembles neural topology. In fact, there is a one-to-one mapping between the ontology of abstraction and the spatial topology of neurons. In the figure below, the solid lines with arrows leading away from each box represent the extension of an abstraction (and the concept it partially represents). They also represent a neurons axon. The dotted lines with arrows pointing toward each box represent the intension of an abstraction (and the intension of all the abstractions that represent the concept represented by the box). They also represent a neurons dendritic trees. Just like the direct and indirect representations, this diagram represents Thing1 as being related to Thing2 by relation R1, and Thing1 being related to Thing3 and Thing4 by Relation R2. When R1's axon fires, it causes synapse R1 to fire at time t. Then Thing2's axon fires at such a time that synapse T2 fires just as the electrotonic potential from synapse R1 reaches the dendritic location of T2. The electrotonic potentials then superimpose and sum and their sum flows down the dendritic tree to the axon hillock of Thing1 and arrives at some time ta. Meanwhile R2's axon fires which causes synapse R2 to fire and send electrotonic potential down the dendritic tree towards Thing1. Synapse R2 fires at just the right time so that its electrotonic potential will reach the axon hillock at time ta. Sometime after synapse R2 fires, Thing3 and Thing4 fire their axons at such a time that the electrotonic potential from their synapses also reaches Thing1s axon hillock at time ta and superimposes with the other electrotonic potentials. Because the electrotonic potentials from synapses R2, T3, and T4 are all spatiotemporally correlated, they superimpose at the position they intersect their common dendritic path and the integrated sum of the superimposed electrotonic potentials travel down to the Thing1s axon hillock together. Of course if the relative firing times are not correct, then Thing1 doesn't reach its activation threshold and doesn't fire its axon. If the relative synaptic firing times are correct, then the electrotonic potential does reach Thing1's activation threshold and it fires its axon. The firing of thing1's axon means the intensional conditions that define how Thing1 is related to Thing2 by R1, and how Thing3 and Thing4 are related to Thing1 by R2 were met. Therefore the firing of Thing1's axon represents the existence of the abstraction that represents Thing1. It signals the satisfaction of Thing1's intensional conditions and thus represents the relation between the intensional meaning of Thing1's definition and its existence. The firing of the axon doesn't encode any information directly. However, when fired, it signals the occurence of an instance of the abstraction represented by Thing1. Therefore it can transmit an arbitrary amount of meaning without the need to encode any information. That means the size of the representation is constant, irrespective of the complexity of the set of abstract relations that it represents. The size of the representation is independent of the complexity of whatever it represents in univeral representations. In addition, this means there is no neural code. There are too many other representational and computational advantages to cover here and we haven't discussed the prerequisites needed to understand them. I will cover them when I discuss the neural knowledge representation in more detail in a future blog.

We have now introduced the direct indirect axis of representation. We learned that there are three fundamental types of representation along the direct indirect axis; direct representations, universal representations, and indirect representations. The representation of existence is a direct representation. The representation of thought is a universal representation, giving thought the power to represent things directly and indirectly simultaneously. The representation of information is an indirect representation. The representation of information provides the basis for natural language, communication, symbolic logic, computer programs, and mathematics among other things.

While these descriptions do not cover the direct - indirect axis of representation in exhaustive detail, they do provide enough of an introduction to make it worthwhile to move on to describe the second principal axis of representation – the intensional – extensional axis.

The Intensional - Extensional Axis of Representation

2009-01-21T17:08:00.000-08:00

The Intensional – Extensional Axis Of Representation

The second principal axis of representation is the intensional – extensional axis. All representations have intensional and extensional aspects. The intension of a representation can be stated equivalently as that set of conditions which must be satisfied by any object, within the given universe of discourse, for the representation to exemplify the object. If an object satisfies the intensional conditions, then it is an exemplar of the object.

In indirect representations, the intension of a concept represents the syntactic definition of that which it represents. In indirect representations, the epistemic meaning of a concept can be inferred or interpreted from the representation of the concept’s intension by an intelligent observer, but not by the object itself. For example, a dictionary definition cannot read itself. It does not understand the meaning of the words it contains. A computer does not, and cannot, understand the meaning of its data. Indirect intensions represented using information contain syntax but not semantics. Consequently, the representation of indirect intensions using information is incomplete.

In direct representations, Representation = Existence. Direct representations represent things in terms of how they relate to the things that compose them and in terms of how they relate to those things that affect them in their external environment. The intension is directly composed of the extensions of the set of objects and object relationships that the object being represented is composed of and related to. The existence of the set of objects and object relationships that represent the objects that compose the object being represented and the existence of the relationships between its component objects and those objects it is related to in its external environment directly represent the existence of the object being represented. In a direct representation, the extension IS the representation and existence of the intension. Symbolically we have: Existence(Extension) = Existence(Intension). This is equivalent to Existence = Representation. In a direct representation, the representation of an objects’ intension encapsulates the representation and thus the existence of the extensions of the objects and object relationships that the object being represented is composed of and related to. (Intensional relations exist between the objects that compose the object being represented and between the object being represented and those it is related to in its external environment). Direct representations represent existence as an nth order relational hierarchy of composition. Objects can be composed of objects that are composed of objects that are composed of objects, to any required degree. Any object can be composed of zero or more objects, each of which may be composed of zero or more objects. The same is true of relations. There can be first order relations between objects: O R O, second order relations between relations: O R(R) O, third order relations: O R(R(R)) O, etc to any required degree. At the most fundamental level of the representation of existence, both the objects and the relations are composed of the same thing and represented the same way, by differences (i.e., asymmetries) in incomplete, inconsistent nonexistence. We’ll have a lot more to say about this when we cover the detailed representation of existence later.

The extension enumerates all members of the set that satisfy the relational conditions specified by the intension.

In a direct representation, the extension represents, and is, the only instance of the object represented by the intension. The existence of the intension IS the existence of the extension. In a direct representation, the cardinality of the extensional set is always 1. The extension represents the existence of the intension. In a direct representation, the extension can be represented by one bit of information, irrespective of the complexity or level of composition of the intension. However, the bit has no meaning in and of itself. Its existence simply signals the existence of the extension, and thus the satisfaction of the intensional conditions represented by the extension. If the intensional conditions are not met, the extension does not exist. This explains why fundamental particles cannot be split and why energy is quantized. It is impossible to divide the fundamental quanta of existence. All quanta exist completely, or not at all. Their representation is always complete and consistent. It is impossible for a quanta to have a partial state of existence. It cannot be part in the universe and part outside it. Creation and destruction of quanta are instantaneous, indivisible events. If the representation of a quanta is made inconsistent or incomplete, it ceases to exist. For this reason, the representation of existence is complete and consistent. It is impossible for it to become incomplete or inconsistent, so there is no need to represent or enforce ontological consistency.

In an indirect representation, the extension enumerates all members of the set that satisfy the relational conditions specified in the intension and that represent exemplars or instances of the object or concept being represented. The members of the extension represent the instances of that which is represented by satisfaction of the intensional conditions, they are not the instances themselves.

A universal representation combines intensional and extensional representation. In a universal representation, the intension is direct, but its extension is indirect. Consequently the intension defines meaning in context from the direct first person perspective. The intension of a direct universal representation defines and understands its own meaning from the first person perspective in context. The indirect extension can be used in multiple contexts and be included as part of the representation of multiple intensions. In this case, the representation of the intension is represented directly by value, but the extension is represented indirectly by reference. This will be covered in much more detail when we derive the representation of thought.

Table 1 provides an overview of the three classes of representation, their relationships, and some examples of things represented by each class.

The representations in column 1 are direct. Direct representations represent the physical existence of everything in the universe. We will refer to representation at the level of physical existence as direct representation, level 1 representation, type 1 representation or existential representation.

The representations in column 2 are universal; thus, they are both direct and indirect. Universal representations are used to represent thought. In the rest of this book, universal representations will be called type 2 representations. We will also refer to representation at the level of thought as level 2 representation.

The representations in column 3 are indirect. Indirect representation is the type of representation used to represent information. Most human generated representations are of this type. This type of representation is required for communication. It is used for logic, mathematics, writing, speaking, drawing, and computation. Indirect, or information based representations will be called type 3 representations. Representation at the level of information will also be called level 3 representation.

1-Direct

(Existence)

2 –Universal

(Thought)

3 –Indirect

(Information)

A -Intensional

A1
:Direct*

Intensional

Representation
of:

Conservation
of nonexistenceà

Symmetry,
Conservation of Energy, Quantum Mechanics, General Relativity, Physics

A2:Universal*

Intensional

Representation
of:

Meaning
(Direct),

Neurons’
Dendritic Trees, PostSynaptic Terminals

A3:Indirect*

Intensional

Representation
of:

Logical
Predicates,

Mathematical
Axioms, Laws of Physics

B- Universal

B1:Direct*

Universal

Representation
of:

Evolution of the universe.
Existence=

Representation

B2:Universal*

Universal

Representation
of: Thought: Neurons, Abstractions, Concepts, Qualia, Consciousness,

Cogito
Ergo Sum

B3:Indirect*

Universal

Representation
of:

First
Order Predicate Logic, Mathematics, Knowledge Representations

C -Extensional

C1:Direct*

Extensional

Representation
of:

Existence
of the universe

C2:Universal*

Extensional

Representation
of:

Existence
(Indirect),

Neurons’
Axonal Tree, Presynaptic Terminals

C3:Indirect*

Extensional

Representation
of:

Mathematical
Sets

Table 1: Types of Representation

Intensional Representation

2009-01-21T17:01:00.000-08:00

Intensional Representation

The intension of a representation often takes the form of a definition. For example, in the domain of mathematics, an intensional definition is a function. For example, we can define a successor function S that takes an integer argument and returns the integer + 1.
int S(int i)
{
return i + 1;
}

By using this simple function, and a single input of 1, we can inductively define the infinite set of Natural numbers by repeatedly calling the successor function using the output from its previous evaluation as the input to its next evaluation. If called an infinite number of times, the successor function will function as a generator and it will generate the infinite set of Natural numbers.

int i = 1;
for (;;) // repeat forever
{
i = S(i);
}

In this example, the intensional definition would include the definition of the successor function S, the initial input value of 1, and the rule specifying that the successor function be called repeatedly using its output as its next input. The extension would be the entire infinite set of Natural numbers. We can generalize this example to allow intensional definitions to include more than one function, and/or to include generalized functions. For example, we can create intensional definitions that include operators; i.e., functions that take functions and other types of mathematical objects as arguments. For example, an operator could take tensors, or matrices, or even matrices of operators as arguments. Our operators could take any number of any type of mathematical arguments and return any number of mathematical results of any type. Integrals and derivatives are simple examples of mathematical operators.
Intensional definition also applies to rules or sets of axioms that generate all members of the set being defined. For example, an intensional definition of "square number" can be "any number that can be expressed as some integer multiplied by itself." The rule -- "take an integer and multiply it by itself" -- always generates members of the set of square numbers, no matter which integer one chooses, and for any square number, there is an integer that was multiplied by itself to get it.

Similarly, an intensional definition of a game, such as chess, would be the rules of the game; any game played by those rules must be a game of chess, and any game properly called a game of chess must have been played by those rules.

Intensional definitions can take many forms. They need not be logical or mathematical. A dictionary definition of a word is an intensional definition. A set of rules is an intensional definition. For example, an intensional definition of physics consists of the scientific laws of Physics.

If a set contains all possible instances of a logical predicate, that set represents the extension of the predicate. The predicate represents the intensional definition of the set. An intensional definition defines the necessary and sufficient conditions for belonging to the set being defined.
For example, an intensional definition of "bachelor" is "unmarried man." Being an unmarried man is an essential property of something referred to as a bachelor. It is a necessary condition: one cannot be a bachelor without being an unmarried man. It is also a sufficient condition: any unmarried man is a bachelor.

Extensional Representation

2009-01-21T16:53:00.000-08:00

Extensional Representation

The extension of a representation defines things in a different way. An extensional definition defines by enumerating or listing everything that falls under that definition -- an extensional definition of "bachelor" would be a listing of all the unmarried men in the world. Extensional definitions are frequently represented by sets. For example, in the case of our bachelor example, the extensional definition of bachelor would be the set of all bachelors in the world. If we simply listed all the bachelors in the world, this would be an indirect extensional representation. If we rounded up every bachelor in the world and put them all in a large room together, and ensured that the room contained no non-bachelors, then the contents of the room would be the direct extensional representation of bachelors.

Differences between Extensional and Intensional Representation
Intensional definitions are best used when something has a clearly-defined set of properties, and it works well for sets that are too large to list in an extensional definition. It is impossible to give an extensional definition for an infinite set, but an intensional one can often be stated concisely -- there is an infinite number of even numbers, impossible to list, but they can be defined by saying that even numbers are integer multiples of two.

Definition by category and differentia, in which something is defined by first stating the broad category it belongs to (i.e., its common or shared properties) and then distinguished by its differentia (i.e., it’s private or unshared properties), is a type of intensional definition. As the name might suggest, this is the type of definition used in Linnaean taxonomy to categorize living things, but it is by no means restricted to biology. Suppose we define a miniskirt as "a skirt with a hemline above the knee." We have assigned it to a genus, or larger class of items: it is a type of skirt. Then, we have described the differentia, the specific properties that make it its own sub-type: it has a hemline above the knee.

Beyond Information

2009-01-17T16:29:00.000-08:00

BEYOND INFORMATION
The Representation of Existence and Thought

Abstract
This paper argues that humanity has only explored one of three possible forms of representation. Logic, set theory, mathematics, information, and human communication are all indirect forms of representation. The existence of indirect representation implies the existence of its converse, direct representation. A direct representation represents particulars from the first person direct perspective of each particular itself, instead of from the third person indirect perspective of an observer. If direct and indirect representations exist, then to complete the powerset of representation, a third form of representation should exist that is universal; i.e., both direct and indirect[1]. This paper argues that the universe itself is a closed, consistent, and complete direct representation. It argues that the representation of thought is a closed, consistent, and complete universal representation. It argues that information cannot be the correct foundation for the representation of existence because it would violate causality. It identifies the immaterial bivalence responsible for the direct representation of existence, and in doing so, identifies the first cause of symmetry, the first cause of all forms of energy, and a new conservation law more fundamental than the law of conservation of energy. It also identifies the universal bivalence responsible for the representation of thought. It identifies the representational basis for the first person direct relation between meaning and existence at all levels of abstraction in all contexts. It identifies a single universal of computation responsible for the direct neural processing and representation of all perception, awareness, understanding, meaning, and consciousness. It also explains how to create formal representations that can represent everything in the universe and avoid the adverse consequences of Gödel’s Incompleteness theorems. It concludes by recommending the creation of very high priority research programs to create new axiomatic foundations for the direct representation of existence and the universal representation of thought.

[1] To complete the Powerset of representation, a null representation would also exist, but it is uninteresting.

Introduction

2009-01-17T16:26:00.000-08:00

Introduction

Our species uses information as the basis for the representation of all communication. Humans have spent about 2,400 years developing logic, mathematics and science based on information and it has served us well. We have been able to develop theories and scientific laws that allow us to predict the outcome of experiments, develop useful technologies, and understand quite a bit about the composition and function of the universe. Our successes have led most to believe that information is the only possible basis for representation. In fact, the philosophy of information goes so far as to posit that at the very deepest levels, existence itself is derived from bits and based on the representation of information. [1] This paper provides strong arguments to the contrary. It presents a convergent argument that the representation of existence is direct. It argues that the incompleteness of mathematics arises precisely because mathematics is an indirect representation. It argues that mathematics is not isomorphic to the direct representation of existence. Moreover, it argues that it is impossible for mathematics to represent existence directly because mathematics itself is based on the indirect representation of set theory. Representing the direct representation of existence using an indirect representation is incomplete and excessively complex. This paper proposes a direct representation of existence as an alternative to its indirect representation using information. It also identifies the first cause of symmetry and proposes a new conservation law that is more fundamental than the law of conservation of energy.

This paper also argues that the representation of thought is both direct and indirect, and that the brain has no need to use, nor does it use, information to represent or encode thought. We think directly, from the first person perspective in context as in Cogito Ergo Sum. It is not possible to think from the first person direct perspective in context using a third person indirect context free representation. It would be combinatorially too complex, and there would be no way to ground semantic meaning. A brief introduction to the representation of thought is presented. The paper concludes by recommending the creation of high priority research programs to formulate new axiomatic set theories for the direct representation of existence and the universal representation of thought. The former should allow us to accelerate development of theoretical physics exponentially. The latter leads directly to the creation of sentient computers, improved methods for teaching, improvements in treating brain injuries and mental illness, and eventually, a substantial increase in human intelligence.

Keeping Things in Perspective

2009-01-17T16:23:00.000-08:00

Keeping Things in Perspective

Humanity would do well to keep things in perspective. Human beings are only one species among millions on a single planet circling one star in a very large universe. According to the latest scientific estimates, the universe is between 13.60 and 13.84 billion years old.[2] Anatomically modern humans first appear in the fossil record in Africa about 130,000 years ago, although studies of molecular biology give evidence that the approximate time of divergence of homo sapiens sapiens from the common ancestor of all modern human populations was about 200,000 years ago.[3][4][5] Even if we use the earlier date, our species appeared on earth approximately 13.7 billion years after the beginning of the universe. Our entire species has existed for less than 0.0015% of the age of the universe.

Existence cannot represent itself indirectly from the perspective of an observer. Even if it could, existence has no need to use a context free, fixed symbolic encoding to provide a shared basis for the communication of information between particulars in existence. Why should the requirements for the representation of human communication be the same as those for the representation of existence? What is the probability the representation of information our species uses for communication, logic, mathematics, and science just happens to be the same as the representation the entire universe uses to represent itself?

Information is an Indirect Representation

2009-01-17T16:20:00.000-08:00

Information is an Indirect Representation

The representation of information enables communication between observers. It describes things from the third person indirect perspective of an observer. Therein is the problem. The representation of existence is direct. Existence cannot represent itself indirectly from the third person perspective of an observer. Existence is logically prior to observation. Something has to exist before it can be described using information. Particulars in existence can only represent themselves directly from their own first person direct perspective. In addition, because information must describe things from the third person indirect perspective of an observer, it must use a fixed context free encoding to provide a shared basis for the communication of meaning between observers using a shared communication protocol. The purpose of the representation of existence is the direct physical representation of existence, not the indirect communication of information about existence to an external observer. Consequently, the representation of existence does not need to use a fixed context free encoding, and it categorically does not need to represent itself abstractly, or indirectly.

Mathematics is proven incomplete by Gödel’s Incompleteness theorems.[8,9,10] Mathematics is incomplete because it is an indirect representation. Indirect representations are incomplete because they cannot represent anything directly. That means mathematics cannot represent itself directly. It is impossible for mathematics to represent things directly because it is based on axiomatic set theory. The most commonly accepted theory for the foundation of mathematics is the Zermello- Fraenkel, with Axiom of Choice, or ‘ZFC’ set theory. [7] There are many alternative set theories, but they all have one thing in common. They are all indirect representations.

Set Theory is an Indirect Representation

2009-01-17T16:09:00.000-08:00

Set Theory is an Indirect Representation

Axiomatic set theories represent the universe of mathematics from the third person indirect perspective of an observer. Set theory is an indirect representation. The most fundamental concepts of set theory reflect this. For example, set members can be atoms or other sets. Atoms are references for things in the real world, or references for abstract concepts like numbers. The references can represent anything we like, but they are indirect because they are references; they are not the things they represent, they are only references for things that exist. References typically take the form of a label or a name. For example, the set {barry} contains the name ‘barry’. ‘barry’ is a reference for the person named barry. It is not the human being named barry or a direct representation of barry as a human being because it does not have to include the representation of all barry’s components; i.e., barry’s arms, legs, skin, teeth, hair, muscles, molecules, and all their relationships and interactions.

The most fundamental relations of set theory reflect the fact that it is an indirect representation. The set membership operator is not transitive.[6] For example:

2 is a member of the set {1,2}

And {1,2} is a member of the set {{1,2},{3,4}}

but 2 is not a member of the set {{1,2},{3,4}}.

This means set membership does not represent the ‘is part of’ relation. If the representation of set theory were direct, then the set membership relation would be transitive because transitive whole-part relationships are fundamental to the ontology of existence.

Everything that exists in the universe is composed of smaller more primitive things. The elements or components that compose each thing must themselves come into existence prior to the existence of those things they compose. We see this pattern throughout Physics, and throughout the known history of the physical evolution of the universe. Those smaller things are themselves composed of smaller things until we reach the level of so-called "indivisible" fundamental particles. However, the hierarchy of decomposition doesn't stop there. The "indivisible" fundamental particles are not indivisible in an absolute sense. Strictly speaking, they are not even particles in an absolute sense. The fundamental particles are themselves composed of energy fields. Matter is composed of energy. All types of energy fields, and indeed, space-time itself, are composed of zero point quantum field configurations. Ultimately, at the lowest level of physical existence, space-time, all forms of energy, and all forms of matter are composed from the direct representation of compositions of zero-point energy field configurations. The zero-point energy field is the closest thing to non-existence there is. For that reason, I refer to it as "incomplete nonexistence".

Set theory’s equality relation ‘=’ also reflects the indirect representation of sets. In set theory, 1 is not equal to {1} because the former refers to the abstract concept ‘1’, whereas the latter refers to the set whose element is ‘1’. In a direct representation, it would not be possible to distinguish 1 and {1}. In set theory {1, 2, 3} = {1, 2, 1, 3} by definition, because identity is by reference, not by value. In set theory, the two occurrences of ‘1’ in {1, 2, 1, 3} are considered to be the same object because they refer to the same object. This occurs becuase the representation of sets is by reference. Again, this could not happen in a direct representation. In a direct representation, representation = existence. In a direct representation, everything represents itself by its direct existence, or for the purposes of computation, by a one-to-one proxy with unique identity that represents its existence. In a direct representation, the representation of every particular in existence is a singleton. Direct representations cannot represent things indirectly, but they can represent everything that exists in the direct representation completely and consistently. The complement of an incomplete, indirect representation is a complete direct representation. Mathematics is mathematically incomplete precisely because it is based on axiomatic set theory, and as currently formulated, axiomatic set theory is an indirect representation. By creating a new form of axiomatic set theory based on direct representation, we will be able to create a new kind of mathematics that is absolutely complete, in the sense that it would have the ability to represent absolutely anything in the universe completely and consistently. This is the only way to eliminate Godelian incompleteness in mathematics, and in computation.

Set theory represents the set with no members as { }, the empty set. It must do so because set theory is an indirect representation. It does not represent existence directly; it represents it indirectly using sets so it must represent empty sets. In a direct representation, representation = existence. Therefore, the empty set does not exist in the real physical universe that is existence; i.e., the representation of nonexistence is nonexistent. An indirect representation, like the representation of information, or the representation of mathematics requires a representation of nonexistence (via the empty set), but true, i.e., "complete" or "universal" non-existence has no physical existence in the physical universe of existence. The direct representation of nonexistence is a nonexistent representation. That is why nonexistence is physically nonexistent. Like all things in direct representation, non-existence represents itself. While "complete", universal nonexistence can have no physical existence (due to the finite speed of light), "local"; i.e., "incomplete", non-existence does have physical existence in the universe. It is what lies inside the singularity inside the event horizon of every black hole.

From the foregoing discussion, it should be clear that set theory is poorly suited for the representation of phenomena whose existence is based on direct representation. Set theory can only represent direct representation indirectly. All forms of indirect representation are incomplete in an absolute sense, i.e., in the sense of being able to completely represent everything in the universe. That means all representations based on indirect representation are incomplete. That includes all of logic, mathematics, and all computation and communication based on the theory of information. Think hard about the consequences of that! It means we are blinded by information. Our logic, mathematics, computation, and communication are all necessarily incomplete. There are some things in the universe they cannot reach, fully describe, or fully compute. There are limits to what can be described using the representation of information. Humanity can do better. We can overcome the complexity and incompleteness limitations inherent in the indirect representation of information. The existence of the physical universe proves that such a direct representation exists. In fact, all we need to do is understand the neural representation of thought and knowledge. It is possible. I have already done so. The brain uses an internal knowledge representation that is both direct and indirect. The brain's knowledge representation is based on the direct representation of abstraction. The physical topology and morphology of neurons are a direct physical representation of abstraction. We think abstractly because our neurons represent the world directly in terms of abstractions. Because it is a direct representation, the brain's internal knowledge representation is complete, consistent, and has constant complexity. Our brain has the inherent internal capability to represent anything that can exist in the universe abstractly. The bottleneck lies in our ability to communicate what our brain really represents through the incomplete external limited bandwidth communication channel provided by information.

The universe is complete by definition. Since the universe exists, it must have a representation in existence. The completeness of the physical existence of the universe provides absolute proof that the representation of the physical existence of the universe cannot be based on information. That makes it very complex to represent existence. It makes it impossible to directly represent thought from the first person direct perspective. There is no direct basis for semantic grounding using an indirect representation. First person direct context dependent representation and understanding of meaning cannot be based on a third person indirect context free representation.

In principle, all of mathematics is based on axiomatic set theory. That means all of mathematics is indirect. The representation of the universe itself is direct. That means we are trying to represent existence using a representation whose most fundamental elements, relations, and ontology are not isomorphic to that of existence. The universe of mathematics is not isomorphic to the universe of existence. The universe of mathematics is more flexible and more general than the direct representation of existence. While indirection increases generality, it is not without cost. The cost of indirection is incompleteness and a combinatorial increase in complexity. The cost of that incompleteness and increased complexity is incredible. It is the reason the mathematics used to describe physics is complex. It is the reason it has taken humanity more than 2000 years to reach our present understanding of physics and indeed, essentially all of science.

First Order Logic is an Indirect Representation

2009-01-17T16:06:00.000-08:00

First Order Logic is an Indirect Representation

First order propositional logic represents everything from the third person indirect perspective of an observer. Sentence letters represent particulars indirectly. They are labels for abstract concepts, or labels for objects in the real world. The same sentence letters may have different meanings in different contexts. This could not happen in a direct representation. The concepts of ‘True’ and ‘False’ are themselves labels for abstract concepts.

The representation of the universe is direct and physical. It is concrete. It is not abstract, and it is not indirect. First order logic fails to distinguish between the indirect, abstract representation of thought about reality, and the direct, concrete representation of reality. It fails to distinguish the difference between an indirect representation of existence and the direct physical representation of existence itself. In hindsight, this was probably unavoidable. We experience and think about the world indirectly and abstractly. Because thought seems to be indirect[1], we attempted to represent everything indirectly. Lacking an understanding of the representation of thought, we did not understand where to draw the line between thought and reality.

Propositional calculus depends on propositional logic. Predicate logic depends on propositional logic. Predicate calculus depends on propositional calculus. Axiomatic set theory depends on predicate calculus. Mathematics depends on axiomatic set theory. “Bits’ represent particulars indirectly. A ‘bit’ is an indirect representation or label for an abstract concept, or for an object in the real world. The same bit may have different meanings in different contexts. Information is composed of and represented in terms of bits, so it too is an indirect representation.

[1] The representation of thought is actually both direct and indirect. This is explained later in this paper.

Information Blindness

2009-01-17T16:02:00.000-08:00

Information Blindness

The fact that our species uses information as its exclusive basis for communication makes our species blind to the possibility that other bases of representation exist. The widespread presumption that information is the only available basis for representation is species centric. In hindsight, our exclusive reliance on indirect representation will prove to be no better than the Ptolemaic geocentric astronomy European and Arabic astronomers mistakenly labored under for 1,393 years prior to the advent of Copernican heliocentric cosmology and the start of the scientific revolution.

Since the time of Ptolemy, physicists have learned not to trust centric points of view. First physicists discovered that the earth was not the center of the universe. Then they discovered that the sun was not the center of the universe. Then they realized that our Milky Way galaxy is not the center of the universe. They have learned that there is no center in space. They have learned that space has no preferred direction and no preferred orientation. However, to this day, physicists are still falling into the trap of relying on a centric point of view. Physicists are still relying on the observer centric point of view of information. They still describe the universe from the 3rd person indirect perspective of an observer. Physical existence doesn't depend on any observer. Why should the physical representation of existence be dependent on the perspective of an observer? Why should physical existence be based on information?

The representation of existence is context dependent, not context free. Particulars in existence always exist in some context. Existence uses a relative relational encoding, not a fixed context free encoding. Most importantly, the representation of existence must be consistent and complete. The entire universe must be represented by a single universe of discourse. There can be no domain limitations. There can only be one ontology and one direct representation of existence for the entire universe. All other alternatives increase complexity combinatorially in the number of representations by making it combinatorially more complex to maintain the consistency and completeness of multiple overlapping representations of existence.

The fact that logic, mathematics, and science have succeeded in representing many different limited fixed domains of discourse using many different formal systems each with its own representation, its own ontology and its own ontological consistency rules is not a logically sufficient basis for assuming that information is the basis for the representation of the entirety of existence itself. The ability to represent limited domains of existence is not the same as the ability to represent all of it at once. Representations based on information are incomplete. They are domain limited. They are complex. They are brittle and fail easily in the face of unexpected input. They are inefficient. Most significantly, they require a priori knowledge of what is to be represented before a suitable representation can be formulated. Existence is logically and physically prior to observation. Therefore, the use of information as the basis for the representation of existence violates causality. Continuing to base all representation on information despite this fact is illogical and wasteful in the extreme. The only logical alternative is to move beyond the representation of information to overcome these problems.

2009-01-17T15:59:00.000-08:00

Viewing the Universe through the Lens of Information

Physics has had many successes. However, it has been unable to answer many of the most basic questions about the universe using information. For example, what force causes a photon to travel through space at the speed of light? What causes that force? How large is that force? How can a photon carry electromagnetic charge when it has no charge? Why are energy and matter quantized? What causes the quantization of energy and matter? What causes like charges to repel and opposite charges to attract? What is time and what causes it? Why does energy exist? What is the first cause of energy? What created the Big Bang? What came before the Big Bang? What created space? What created the dimensions of space? What causes symmetry? Why is symmetry so prevalent in the universe? What ensures the consistency of the Universe? How could an information-based representation ensure the global consistency of existence, given all the different domains of discourse, representations, ontologies, and ontological consistency rules it would seem to require? The fact that we have been unable to answer these most basic questions is a sure sign that we are missing something very fundamental. It is as if we have been trying to analyze and understand the entire universe by looking through the lenses of millions of microscopes, each viewing the universe in a limited spectrum and each having a limited, isolated field of view, each described using its own specialized symbols, models, and languages. Looking thru the incomplete, domain limited lens of information, we cannot see or reach all the squares on the chessboard of reality because the physical representation of the universe itself is not based on information. Information only provides an incomplete, partial representation of reality. We need to go beyond the limitations and constraints of information if we want to understand Physics completely. We need to be able to model and represent all of reality as a complete, consistent, integrated whole in all of its context dependent splendor using a single complete and consistent representation that is isomorphic to the full representation of existence. The same is true of all physical sciences.

2009-01-17T15:56:00.000-08:00

Thought and Information

The fact that we communicate using information is also not a logically sufficient basis to assume that our brains use information as their internal neural basis for the representation of thought. People must communicate with each other using information with fixed encodings to establish a shared basis for understanding via communication using a common alphabet and language. However, the neurons in our brain do not communicate directly with neurons in other people’s brains. Our neurons do not communicate with anything other than the other neurons inside their own nervous system. The nervous system is a closed representational system. Neurons have no need to establish or maintain a public shared basis for the internal communication of information. They are free to use their own private language and their own private encoding. In fact, by removing the fixed encoding constraints required for external communication, neurons can vary their encoding as a function of that which they represent to minimize code length and storage space. They can use a relative relational encoding unique to the current state of knowledge stored in each individual’s brain. They can use a representation that is direct and indirect, instead of one that is only indirect. In fact, neurons must use a representation that is both direct and indirect. Without a basis in direct representation, there is no basis for the first person direct representation and understanding of meaning. Meaning cannot be grounded indirectly. Neurons have physical existence. Existence is a direct representation. Our neurons operate from the first person direct perspective of existence, but because they represent and implement the ontology of abstraction, they also allow us to represent things indirectly, and to communicate indirectly using information. Neurons convert the indirect external representation of information into the direct representation of thought for internal processing. They convert the internal direct representation of thought back into the indirect representation of information for external communication. While this conversion may seem complex or difficult when viewed from the perspective of information, it is a simple matter for the representation of thought[1].

The brains internal knowledge representation operates much faster and much more efficiently when we do not make ourselves think in terms of information. I would like you to try a quick little experiment. Look out your window. See how fast you can recognize all the objects, all their relationships, all the textures, all the colors and understand what you are seeing? Now try to describe the same scene in words and see how many words it takes to describe it to the same level of detail you could perceive, recognize and understand in less than a second. Now give that description to somebody else and see how long it takes him or her to understand the contents of the scene. See how much information was lost in the conversion to information. Now try to describe the same scene using mathematical equations. See how long it takes somebody to understand that, see how much could not be represented using mathematics, and see how much information was lost in the process. That will give you a good feel for the relative efficiency of the brains internal knowledge representation vs. the representation of information. The brain uses the same knowledge representation and computational model for seeing and understanding that scene out your window as it does to think and reason using symbolic information. The difference in efficiency is almost entirely due to the inefficiency of the representation of symbolic information. When we try to represent and understand the universe in terms of symbolic information, we force our brain to continuously translate back and forth between the indirect representation of information and the brains direct native representation it uses internally to reason and think. That slows the brains native thought process tremendously. It also loses just as much information as the difference between looking out your window and understanding the scene in less than a second vs. trying to describe the scene in words or equations and understand it. Humans have a huge untapped potential to increase the speed and depth of comprehension of abstract knowledge and increase intelligence. To unlock this potential, we need to learn the brains’ native representation of thought and teach ourselves to use it directly. Until we do that, we will continue degrading our innate mental capacity by forcing our brain to think indirectly in terms of what for it is a terribly inefficient, complex, symbolic, foreign representation of information.

[1] A paper that describes this transformation in detail is in preparation.

We Must Move Beyond the Representation of Information

2009-01-17T15:48:00.000-08:00

We Must Move Beyond the Representation of Information

The assumption that information is the basis for the representation of existence is incorrect. The assumption that information is the basis for the representation of thought is also incorrect. On what basis do I make these claims?

1) Set theory and the representation of information are indirect. The universe is direct.

2) I have discovered two entirely new classes of representation that are not based on the representation of information. One is combinatorially less complex than the representation of information. It appears to be the direct representation of existence. It provides direct intuitive interpretations for the foundations of quantum physics with minimal complexity. It provides direct answers for many of the deepest unsolved mysteries in Physics. For example, it explains the first cause of symmetry and the cause of the quantization of existence. It explains the cause of the universal consistency and completeness of existence and proves it mathematically. From the axiomatic definition of existence, it derives the meaning of nonexistence, the meaning of infinity, the meaning of universe and their relationships mathematically. The second representation is geometrically less complex than the direct representation of existence. Therefore, it is geometrically combinatorially less complex than the representation of information. It is more powerful than the representation of information, logic, and mathematics. It is complete and consistent. It is the representation of thought. The representation of thought is direct and indirect. Its ontology is isomorphic to neural morphology at the level of individual neurons and at the level of the overall pattern of neural connectivity in the human neocortex. It explains the neural basis for the representation of thought, meaning, perception, awareness and consciousness. Unlike the representation of information, the representations of existence and thought are both provably complete and consistent. The representation of thought is based on the direct representation of the ontology of abstraction. The ontology of abstraction is direct and indirect, and unlike information or logic, it is both intensional and extensional. It consists of a single universal of computation, a single representational primitive, and a single ontology, all of which are represented by the same thing. Neurons are isomorphic to the ontology of abstraction. From a high- level perspective, neural connectivity in the human neocortex is logically organized as a top down hierarchy of concepts where each node in the hierarchy contains a bottom up hierarchy of abstractions. The hippocampus is located at the top of the concept hierarchy and the sensory receptors and nerves that control the muscles are located at the bottom. The association cortices are located in the interior. This allows us to think abstractly, it allows us to think conceptually, and it allows us to think in context. It also allows us to represent and understand meaning from the first person direct perspective in context at multiple levels of abstraction simultaneously. Papers that describe both of these representations in detail are currently in preparation.

3) Gödel’s Incompleteness Theorems [8,9,10] prove information based formal systems incomplete. The complement of an indirect, incomplete representation is a direct, complete representation.

4) Indirect formal systems are only complete in domains of discourse of limited size. To avoid incompleteness we must limit and fix the size of the domain of discourse. This causes domain limitations. Domain limitations lead to a combinatorial increase in complexity because they force us to resort to the use of multiple domains, multiple representations, multiple ontologies, and multiple sets of ontological consistency constraints to cover the representation of the universe as a whole. In such a system, there is no known way to ensure the global consistency or completeness of the representation of the universe as a whole.

5) Information is represented from the perspective of an observer. The universe cannot represent itself from the perspective of an observer. Existence is logically prior to observation. From what observers’ perspective could the first thing in the universe have been represented? We know there had to be a first thing. The universe has a lower size limit[1]. Therefore, it is finite. Therefore, time had a beginning. Therefore, there had to be a first thing. If there was a first thing, it could not have had an observer. Furthermore, there could not have been any perspective to view it from because the perspective itself (i.e., spacetime) would have had to preexist. Furthermore, without an observer, there would have been nothing to ask yes-or-no questions, no basis for the formulation of the questions, nothing to measure the results with, and nothing to record the binary answers on or in. Since existence is logically prior to observation, existence had to be created before it was observed. Since information is dependent on an observer, either the representation of existence is not based on information, or existence does not exist. Since the universe exists, we must conclude existence cannot be based on the representation of information.

6) ON.2 It from bit.[1] Otherwise put, every “it” — every particle, every field of force, even the space-time continuum itself — derives its function, its meaning, its very existence (even if in some contexts indirectly) from the apparatus-elicited answers to yes-or-no questions, binary choices, bits. “It from bit” symbolizes the idea that every item of the physical world has at bottom — a very deep bottom, in most instances — an immaterial source and explanation; that which we call reality arises in the last analysis from the posing of yes-no questions and the registering of equipment-evoked responses; in short, that all things physical are information-theoretic in origin and that this is a participatory universe. (Wheeler [1990], 5);

While this argument seems plausible on the surface, it is deeply flawed. First, the premise is ambiguous because it fails to distinguish between the direct physical existence of particles, fields of force and the space- time continuum, and their indirect representation as information. While an indirect, set theoretic, information based description of the function, meaning and existence of particles, fields of force and the space time continuum may be derived from the answers to yes-or-no questions and represented as bits, that representation is only an indirect description, or model, of reality. It is information intended to describe reality indirectly; it is not reality or a direct representation of reality itself. It cannot be a direct representation of reality. The axiomatic definition of ‘set’ makes it impossible for a set to represent reality directly. In addition, the meaning of the information is only in the mind of an observer. The direct representation of the actual physical existence of particles, fields of force and the space-time continuum itself is not abstract. It is not symbolic. It is not based on bits. It is not indirect. It is direct. It is physical. Reality itself is composed of the direct physical existence of fermions, bosons, and their interactions, not bits. Reality is a direct representation, not an indirect representation.

Second, relative to the first thing in existence, who or what is going to formulate the yes-or-no questions?

Third, relative to the first thing in existence, who or what is going to measure, interpret and record the answers as bits?

Fourth, relative to the first thing in existence, where are the bits going to be recorded and stored?

Fifth, relative to the first thing in existence, what is going to interpret their meaning?

Sixth, yes-or-no questions are abstract, but the representation and process of abstraction are not immaterial. The representation and process of abstraction are carried out in the mind of an observer who thinks. Neurons represent thought. Neurons are physical, not immaterial. Therefore, the representation of yes-or-no questions is not immaterial, nor is the representation of the bits by the neurons that represent their answers. Furthermore, if ON.2 argues for the immateriality of the representation of thought, it contradicts ON.1.

ON.2, “It from bit” is almost correct. The fundamental direct physical representation of the universe is bivalent, and at the deepest level, it is immaterial, but the immateriality and bivalence are not based on the answer to yes-or-no questions. The basis for the bivalence is not one or zero or true or false. During the Big Bang there was no apparatus for formulating yes-or-no questions. There were no observers to ask yes or no questions. There were no observers to record any answers. No observer could possibly have existed to observe the creation of the first stars at the time of their creation. The quarks, gluons, photons, electrons, protons, neutrons, and other subatomic particles cannot be physically composed of information. The meaning of the immaterial basis for the bivalence of the universe has been misinterpreted. Therefore, the meaning of the bit has been misinterpreted. As currently defined, the bit is isomorphic to the foundations of mathematics and logic. It is isomorphic to the representation of information and human communication. It is a natural outcome of a formal analysis of mans use of symbolic communication and natural language. Man uses information for communication. We must use information with a fixed context free encoding and publicly understood syntactic rules in order to communicate. Information encoded in the form of English is one of man's communication protocols in the same way information encoded in TCP/IP is one of a computer's communication protocols. The cells in our bodies are not composed of English words, any more than the logic gates in a computer chip are composed of bits. Bits and words are just information. They are just a communication mechanism. That is all they are. Information has absolutely nothing to do with the physical composition of existence. Information is just man's method for encoding, transmitting, storing, recalling, and receiving the data in communication. Information is a way to encode and represent data about physical existence. It is not physical existence itself. It is not fully isomorphic to the direct physical representation of existence.

7) The representation and encoding of information is context free. The representation and encoding of existence are context dependent. Representing direct context dependent systems using indirect context free representations increases complexity combinatorially in the number of contexts (and the number of representations) used to represent them.

8) The representation and encoding of information is indirect in that bits represent that which they encode indirectly; i.e., they are a substitute or label for that which they represent, they are not the thing they represent. The representation and encoding of existence are direct. Representation = Existence. The physical representation of existence is existence; it is not information about existence.

[1] The lower size limit is the Planck length.

Existence Beyond Information

2009-01-17T15:38:00.000-08:00

Existence Beyond Information

The immaterial basis for the representation of existence is nonexistence. There is nothing more immaterial than nonexistence. Nonexistence has no constraints, no boundaries, no dependencies on the existence of numbers, quantity, or dimension, and no dependence on an observer. It has absolutely no domain limitations. It cannot be destroyed. Instead of making mathematics isomorphic to the indirect representation of information and human communication, we need to make it isomorphic to the direct physical representation of existence. Instead of building a Von Neumann Universe from the transfinite recursion of empty sets via nested powersets to create the indirect mathematical universe of ordinals, we need to build a direct set theoretic representation of the universe itself based on transfinite recursion of the fundamental unit of existence. This requires that we redefine the axiomatic concept of set using an ontology isomorphic to that of existence.

The fundamental unit of existence is a quantized nilpotent symmetric difference in nonexistence. At the quantum scale, all matter and energy are quantized. All physical quanta exist fully or not at all. All quanta are created and destroyed instantaneously[1]. At no time are they partly in existence and partly nonexistent. Quanta are the indivisible atomic units of existence. They cannot be subdivided. Quanta are universally, physically, existentially, and completely bivalent. They exist fully, or they do not exist at all. Quanta are also much more general than the answers to yes-or-no questions. As far as we know, everything in the Universe is composed of quanta and their relationships at the deepest level of existence. Thus, a representation based on the transfinite recursion of quanta and their relationships is well founded, complete, and not domain limited. Furthermore, quanta and their direct relationships avoid the need for an observer, they avoid the need to formulate or ask yes or no questions, they avoid the need to measure and interpret the answers to those questions, and they avoid the need to store the answers as bits. Therefore, they avoid the need for the universe to describe itself from the indirect perspective of an observer, and they avoid the consequent violation of causality that entails. Given all the facts above, it is clear that quanta and their relationships are the true basis for the bivalence of existence, not bits.

Existence is not based on the answers to true-or-false questions. It is based on the direct physical existence or nonexistence of quanta and their relationships. The quanta and the relationships between quanta are based on differences in nonexistence. The existence of symmetry, space-time, energy, all forces, and the evolution of the universe itself, are a consequence of the conservation of nonexistence. The conservation of nonexistence is more fundamental and more important in directing the ongoing construction and evolution of the universe than the conservation of energy. It is responsible for the existence of symmetry, all quanta, and all forms of energy, all forms of matter, and all relationships between quanta, energy, and matter.

[1] Creation and destruction occur within a Planck time.

Thought Beyond Information

2009-01-17T15:32:00.000-08:00

Thought Beyond Information

The key idea behind the representation of thought is to represent one and only one thing directly, but that one thing then represents everything else indirectly. The one thing that represents everything indirectly is abstraction. This provides a direct representation of indirect representation. It directly represents everything indirectly. With indirect representations like logic, set theory and mathematics, we attempt to represent everything represented by direct representation indirectly. Logic, set theory and mathematics do just the opposite of what the brain does. Instead of directly representing everything indirectly, logic, set theory and mathematics attempt to indirectly represent everything, directly. It is impossible to indirectly represent everything directly because the indirect representation of everything is too complex and it is inconsistent or incomplete or both. Doing things the other way around, the representation only has to represent one thing completely and consistently. If there is only one thing to represent in a domain of discourse, the only way for it to be incomplete or inconsistent is for it to be incomplete or inconsistent relative to itself. It is impossible for a direct representation based on relative relational encoding to be inconsistent or incomplete[1]. This then allows us to avoid the adverse consequences of Gödel’s incompleteness theorems.

Fortunately, it is possible to represent one thing completely and consistently using information - provided the complexity of that one thing is not too great. Therefore, we can use a computer to indirectly represent the direct representation of one thing, and then use that one simulated direct thing to ‘directly’ represent everything else indirectly. We use the same strategy used by nature in the brain, but it is a little less efficient due to the additional level of indirection. Nevertheless, it still provides the means to represent everything indirectly completely and consistently. It also still has all the same benefits in terms of the geometric combinatoric reduction in complexity and storage size. It allows us to create sentient computers that represent and understand the meaning of information from the first person direct perspective in context.

[1] In a relative relational encoding, the representation and the encoding are fully encapsulated. The encoding itself is a function of that which it encodes. The representation of existence is defined relative to symmetric differences in nonexistence. Nonexistence is the only thing ‘inside’ and ‘outside’ the universe that has no dependencies.

Summary

2009-01-17T15:25:00.000-08:00

Summary

There are three main branches in the tree of knowledge:

Direct Representation
Universal Representation
Indirect Representation

Logic, set theory, mathematics, information, and human communication are all forms of indirect representation.

Formal systems are incomplete because they are indirect representations. Indirect representations cannot represent themselves or anything else directly.

Direct representation is complete and consistent. Direct representations can represent themselves and all that they represent directly.

Everything that physically exists in the universe is represented by a direct representation. This includes the physical existence of neurons and the process of abstract thought, including the thought process that led to the human development of indirect representation. Direct representation led to universal representation which led humanity to the development of indirect representation.

Many of the “unsolved” mysteries and complexities encountered in the physical sciences are due to our attempts to represent complete, direct, context-dependent phenomena using incomplete, indirect, context- free representations. Things are a lot simpler if viewed from the correct perspective using the correct representation.

Existence is a direct representation based on nilpotent symmetric differences in nonexistence. Nilpotent symmetric differences in nonexistence represent all bosons and fermions and all energy relations between bosons and fermions.

It is impossible to destroy nonexistence. This suggests the existence of a new fundamental physical law for the conservation of nonexistence. The conservation of nonexistence is the first cause of symmetry, the cause of energy, the cause of matter, the cause of the conservation of energy, the cause of all forces, and the cause of the evolution of existence.

Universal representation is the most powerful and most compact of the three classes of representation. It is direct and indirect, intensional and extensional, context dependent and context free, and complete and consistent. It is based on the direct representation of the ontology and process of abstraction. The direct representation and process of abstraction represents abstractions and concepts directly and indirectly. It also represents the relation between intensional meaning and extensional existence, and does so in context across all levels of abstraction. It converts the external indirect representation of information to and from the direct internal representation of thought and knowledge.

Recommendations

2009-01-17T15:23:00.000-08:00

Recommendations

Based on the foregoing arguments, we should place very high priority on research in the following areas:

1) We should develop a new axiomatic set theory based on the direct representation of existence, instead of the indirect representation of information. This will complement existing set theories, existing mathematical logic, and existing mathematics and create a complete and consistent mathematics for the direct representation of existence and Physics. It will allow us to understand the nature of existence with combinatorially less complexity than we can by using an indirect, incomplete representation to represent the direct, complete representation of existence. It should accelerate the development of theoretical physics exponentially.

2) We should develop a new axiomatic set theory based on the universal representation of thought. That is, we need to develop an axiomatic set theory that is both direct and indirect. The resulting logic is geometrically, combinatorially less complex then the indirect representation of current set theories and it is complete and consistent. It is the representation of thought. This leads directly to the development of an extension of information theory that provides the basis for the development of sentient computers that will be able to amplify human intelligence in a manner analogous to the way our machines amplify our muscles. In turn, an understanding of the representation of thought will allow us to improve the methods we use to educate our children. It will also improve our ability to treat brain injuries and mental illness. Most importantly, it will substantially increase human intelligence by teaching us how to think directly in terms of our brain’s native knowledge representation, instead of trying to think indirectly in terms of information.

3) We should develop sentient computers and true machine intelligence. This should be done in two steps. First, we should develop sentient computer software simulations. The author of this paper has already developed the mathematical equations required for this advance. This will teach us a lot about how we think. It will also allow us to create sentient computers that can solve problems that are currently beyond the capacity of human intellect. The results of software simulations can also be used as the basis for the development of sentient computer neuromorphic processors.

4) We can embed sentient software, and/or neuromorphic processors in machines and robots to create autonomous machine intelligence.

Bibliography

2009-01-17T15:15:00.000-08:00

Bibliography

1. Floridi, Luciano, "Semantic Conceptions of Information", The Stanford Encyclopedia of Philosophy (Winter 2008 Edition), Edward N. Zalta (ed.), URL = http://plato.stanford.edu/archives/win2008/entries/information-semantic/.

2. "Five-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Data Processing, Sky Maps, and Basic Results". nasa.gov. Retrieved on 2008-03-06.

3. Human Ancestors Hall: Homo Sapiens - URL retrieved October 13, 2006
^ Alemseged, Z., Coppens, Y., Geraads, D. (2002).

4. "Hominid cranium from Homo: Description and taxonomy of Homo-323-1976-896". Am J Phys Anthropol 117 (2): 103–12. doi:10.1002/ajpa.10032. PMID 11815945.

5. Stoneking, Mark; Soodyall, Himla (1996). "Human evolution and the mitochondrial genome". Current Opinion in Genetics & Development 6 (6): 731–6. doi:10.1016/S0959-437X(96)80028-1.

6. Suppes, Patrick. Introduction to Logic. Belmont, CA: Wadsworth International Group, 1957.

7. "Zermelo–Fraenkel set theory." Wikipedia, The Free Encyclopedia. 16 Dec 2008, 21:02 UTC. 11 Jan 2009 <http://en.wikipedia.org/w/index.php?title=Zermelo%E2%80%93Fraenkel_set_theory&oldid=258428352>.

8. Godel, Kurt. “Some metamathematical results on completeness and consistency (1930b)”. From Frege to Godel, A Source Book in Mathematical Logic, 1879-1931. Ed. Jean van Heijenoort. Cambridge, MA: Harvard University Press, 1967. 595-6.

9. Godel, Kurt. “On formally undecidable propositions of Principia mathematica and related systems I (1931)”. From Frege to Godel, A Source Book in Mathematical Logic, 1879-1931. Ed. Jean van Heijenoort. Cambridge, MA: Harvard University Press, 1967. 596-616.

10. Godel, Kurt. “On completeness and consistency (1931a)”. From Frege to Godel, A Source Book in Mathematical Logic, 1879-1931. Ed. Jean van Heijenoort. Cambridge, MA: Harvard University Press, 1967. 616-7.

11. Gruber, Thomas R. "A Translation Approach to Portable Ontology Specifications." Stanford, CA: Knowledge Systems Laboratory Technical Report KSL 92-71, Computer Science Dept., Stanford University (1993)

12. Smith, Preprint version of chapter “Ontology”, in L. Floridi (ed.),
Blackwell Guide to the Philosophy of Computing and Information, Oxford: Blackwell, 2003, 155–166.